Question 1. For each of the following sets, decide whether it is finite, countable, or uncountable. Explain your answer briefly. (1) $P(Q)$

Step 1 ：The set $P(Q)$ refers to the power set of the set of rational numbers. The power set of a set is the set of all subsets of the set.

Step 2 ：The cardinality of the power set of a set with cardinality $n$ is $2^n$.

Step 3 ：The set of rational numbers is countably infinite, which means it has the same cardinality as the set of natural numbers.

Step 4 ：Therefore, the power set of the set of rational numbers has a cardinality of $2^{\aleph_0}$, where $\aleph_0$ is the cardinality of the set of natural numbers.

Step 5 ：This is the cardinality of the set of real numbers, which is uncountable.

Step 6 ：Therefore, the set $P(Q)$ is uncountable.

Step 7 ：Final Answer: The set $P(Q)$ is \boxed{\text{uncountable}}